Global exponential stability of Cohen-Grossberg neural networks with distributed delays

In this paper, the globally exponential stability of Cohen-Grossberg neural networks with continuously distributed delays is investigated. New theoretical results are presented in the presence of external stimuli. It is shown that the Cohen-Grossberg neural network is globally exponentially stable, if the absolute value of the input vector exceeds a criterion. Comparison between our results and the previous results admits that our results have an extended application. A numerical example is supplied to illustrate the effectiveness of our approach.

[1]  Liang Jin,et al.  Absolute stability conditions for discrete-time recurrent neural networks , 1994, IEEE Trans. Neural Networks.

[3]  Sannay Mohamad.  Global exponential stability in DCNNs with distributed delays and unbounded activations , 2007 .

[4]  Xuyang Lou,et al.  Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Wei Wu,et al.  Improved Sufficient Conditions for Global Asymptotic Stability of Delayed Neural Networks , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Lin Wang,et al.  Stability of Cohen-Grossberg neural networks with distributed delays , 2005, Appl. Math. Comput..

[7]  Libin Rong.  LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay , 2005 .

[8]  Wei Wu,et al.  Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neurocomputing.

[9]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[10]  Wei Wu,et al.  Global exponential stability of Cohen-Grossberg neural networks with distributed delays , 2008, Math. Comput. Model..

[11]  Jinde Cao.  A set of stability criteria for delayed cellular neural networks , 2001 .

[12]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[13]  S. Arik.  Stability analysis of delayed neural networks , 2000 .

[14]  Jianhua Sun,et al.  Global asymptotic stability of Cohen–Grossberg neural network with continuously distributed delays , 2005 .

[15]  Stephen Grossberg,et al.  Nonlinear neural networks: Principles, mechanisms, and architectures , 1988, Neural Networks.

[16]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.

[17]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[18]  B. Cui,et al.  Global asymptotic stability of Cohen–Grossberg neural networks with constant and variable delays , 2007 .

[19]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[20]  Jianhua Sun,et al.  Global exponential stability and periodic solutions of Cohen–Grossberg neural networks with continuously distributed delays , 2005 .

[21]  Zhigang Zeng,et al.  Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , 2006, Neural Networks.

[22]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[23]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

[24]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[25]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .